Intersection of a plane and cylinder

In summary, the intersection of a plane and cylinder is the set of all points where the plane and cylinder intersect, creating a common boundary. This boundary can be a single point, a line, or a curve depending on the orientation of the plane and cylinder. The intersection can have a maximum of two points, with different types of intersections including a point, line, circle, ellipse, parabola, and hyperbola. It can be calculated by solving the equations of both the plane and cylinder simultaneously, and is used in various applications such as engineering, architecture, and computer graphics for creating 3D models, designing structures, and calculating volumes. It is also used in real-life applications such as the intersection of roads and tunnels in civil
  • #1
Stevecgz
68
0
Question: Find a parametric representation for the curve resulting from the intersection of the plane 3x + y + z = 1 and the cylinder x^2 + 2y^2 = 1.

What I did:

x = cost
y = sint/sqrt(2)
z = -3cost - (sint/sqrt(2)) + 1

I think I'm doing this correctly but the answer seems too easy for this type of assignment. Hoping someone could look it over and tell me if I'm missing something. Thanks.

Steve
 
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  • #2
It looks alright to me.
 
  • #3
Thanks d_leet.
 

What is the definition of the intersection of a plane and cylinder?

The intersection of a plane and cylinder is the set of all points where the plane and the cylinder intersect, creating a common boundary. This boundary can be a single point, a line, or a curve depending on the orientation of the plane and cylinder.

How many points can the intersection of a plane and cylinder have?

The intersection of a plane and cylinder can have a maximum of two points. If the plane is parallel to the base of the cylinder, the intersection will be a line. If the plane is perpendicular to the base, the intersection will be a circle.

What are the different types of intersections between a plane and cylinder?

The different types of intersections between a plane and cylinder are a point, a line, a circle, an ellipse, a parabola, and a hyperbola. The type of intersection depends on the orientation and position of the plane and cylinder.

How can the intersection of a plane and cylinder be calculated?

The intersection of a plane and cylinder can be calculated by solving the equations of both the plane and cylinder simultaneously. This will give the coordinates of the points where the two surfaces intersect.

What applications use the intersection of a plane and cylinder?

The intersection of a plane and cylinder is used in various fields such as engineering, architecture, and computer graphics. It is used to create 3D models, design structures, and calculate volumes of objects. It is also used in real-life applications like the intersection of roads and tunnels in civil engineering projects.

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